11 plus Transformations questions

What a Transformations question looks like

Transformations is a geometry topic in 11 plus maths. A point or a shape is moved, and the question asks what the move does to it: slid across the grid (a translation), flipped over a mirror line (a reflection) or turned about a fixed point (a rotation). Its two nearest neighbours ask something else: Coordinates & Position is mostly about reading and plotting where things sit, and 2D Shapes & Properties about naming a shape from its properties, whereas Transformations is about what changes and what stays the same when a shape is moved.

The topic covers more than those three moves. Some questions give a before and an after and ask which single move was made. Some ask how many lines of symmetry a shape has, or which shape looks the same more than once in a full turn. Some are about tiling: how many small squares cover a rectangle exactly, or why regular pentagons cannot cover a floor without gaps. Compass points and clock hands turn up as well. Making a shape bigger or smaller does not. Most are drawn on a numbered grid with the point or shape marked on it, so a child can count squares.

Example one: reflecting a point in a mirror line

Point S is at (3, 7). It is reflected in the line y = 5. What are the new coordinates of S?

The grid runs 0 to 8 across and 0 to 10 up. S is a dot at 3 across and 7 up, and a straight line crosses the whole grid at the height marked 5. That line is the mirror.

The mirror is flat, so the point only moves up or down and its across number stays at 3. S sits 2 squares above the line, because 7 take away 5 is 2. Count 2 squares below the line instead: 5 take away 2 is 3.

The answer is (3, 3).

The tempting option is (3, 9): the 2 squares counted correctly, then measured the wrong way, which leaves the point on the same side of the mirror. A flip always crosses the line. The other trap is (3, 5), the point stopped on the mirror line itself.

Example two: which move was it?

Other questions run the other way round, giving a shape’s corners before and after and asking what happened.

Compare the two numbers for each corner. The first never changes: 2 stays 2, 4 stays 4, 4 stays 4, so nothing has moved left or right. The second falls by 4 every time: 5 to 1, 5 to 1, 7 to 3.

The answer is a translation of 4 squares down.

A flip in the line y = 3 is the tempting wrong option, and it survives the first two corners: P and Q each sit 2 above that line and land 2 below it. It fails on R, which sits 4 above the line and would land at (4, -1), not (4, 3). The rule has to hold for every corner, not just the first. Choosing a translation 4 squares up is the other easy slip: the numbers are getting smaller, so the shape has gone down.

Example three: a turn with no grid

Maya is facing North. She makes a quarter turn anticlockwise. Which direction is she facing now?

Picture a compass: North at the top, East on the right, South at the bottom, West on the left. Anticlockwise is the way a clock’s hands do not go, so the turn goes to the left, one place round.

The answer is West.

East is the option that catches children: the same size of turn, made the other way. Direction goes wrong far more often than size does. Papers write this turn as 90 degrees, and clock questions do the same job in twelfths, so a minute hand at the 12 turning two twelfths clockwise finishes at the 2.

How to answer it

1. Name the move in your own words first: a slide, a flip or a turn. If the question gives a before and an after instead, decide which of the three it was before reading the options.
2. Find the fixed thing the move works from: the mirror line for a flip, the centre for a turn, the squares across and down for a slide.
3. Take one point at a time and count squares rather than judging by eye. For a flip, count how far the point is from the mirror line, then the same distance again on the far side.
4. Check the number that should not change. A flat mirror line leaves the across number alone and an upright one leaves the up number alone.
5. If the question gives a whole shape, test the move on a second corner. A rule that only works for one corner is not the rule.

Common mistakes

• Flipping the wrong way. Adding the 2 squares instead of subtracting them turns (3, 7) into (3, 9), still on the same side of the line. A reflection has to cross the mirror.
• Stopping on the mirror line. The point travels twice its distance from the line, not once, so an answer sitting on the line is always wrong.
• Changing both numbers in a flip. A reflection changes one of the two, never both. Turning (2, 3) into (-2, -3) is a half turn about (0, 0), and it is the standard wrong option when the mirror is an axis.
• Counting a rectangle’s diagonals as lines of symmetry. A rectangle has 2, one across the middle and one down. Fold it along a diagonal and the halves do not match. Diagonals only work when all four sides are equal, in a square, which is why 4 catches most children.
• Assuming every shape tiles. Squares and regular hexagons do. Regular pentagons do not: each corner is 108 degrees, which does not divide exactly into the 360 degrees of a full turn, so three pentagons meeting at a point leave a gap.

How to practise 11 plus Transformations questions

Squared paper does more for this topic than any amount of reading about it. Ask your child to plot the point, draw the mirror line, then fold or turn the paper to check the answer they worked out in their head, because the checking is where it sticks. Tracing paper earns its place for turns, laid over the shape with a pencil point held on the centre. Little and often suits a topic built on a handful of rules, which is the pattern we set out in how much 11 plus practice a child needs each day. 11+ Daily has a Transformations project alongside the other geometry topics, on laptop, tablet or phone, and the full list is on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the maths bank has been re-checked in rounds.

Questions parents ask